Modeling of the Transistor Vertical Cavity Surface Emitting Laser
by
Behnam Faraji
B.Sc., Sharif University of Technology, 2002 M.Sc., Sharif University of Technology, 2004
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTSFORTHEDEGREEOF
DOCTOR OF PHILOSOPHY
in
The Faculty of Graduate Studies
(Electrical and Computer Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) May 2011 c Behnam Faraji 2011 Abstract
The direct modulation of semiconductor lasers has many applications in data transmission. However, due to the frequency response it has been chal- lenging to use directly modulated lasers for high speed digital transmission at bit-rates above 10 Gbps. With this in mind, designing a laser with a large modulation bandwidth to be used in high data-rate optical links is very important. Transistor lasers (TLs) are a potential candidate for this purpose.
Based on these motivations, the main focus of this PhD research is on understanding the physics of the TL and predicting its performance. A detailed model that correctly incorporates the transistor effects on laser dynamics did not exist. The previous models do not differentiate between the bulk carriers and the quantum well (QW) carriers in the rate equations, do not include the effects of the capture and escape lifetimes in the QW, and significantly overestimate the bandwidth.
To account for these phenomena, a model has been developed to study the dynamics of the TL. The model is based on the continuity equation in the separate confinement hetero-structure region of the conventional laser and the base region of the TL. It uses the quantum mechanical escape and capture of carriers in the quantum well region and the laser rate equations to
ii Abstract model the laser operation. The model has been used to gain insight into the conventional separate confinement hetero-structure lasers, and the results of the model have been compared with the experimental results obtained for
850 nm vertical cavity surface emitting lasers (VCSELs). Analytical expres- sions have been derived for DC and AC parameters of the TL operating in common-base and common-emitter configurations. It has been shown that the TL operating in the common-emitter configuration has a similar mod- ulation bandwidth as a conventional laser (∼ 20 GHz). The common-base configuration, on the other hand, has a very large small-signal modulation bandwidth (> 40 GHz) due to bandwidth equalization in the TL. The large- signal performance of the TL has been studied. Finally, it has been shown that the common-emitter configuration with feedback has improved band- width by a factor of 1.5 in high bias currents.
iii Preface
Some parts of this thesis are based on several manuscripts, resulting from collaboration between multiple researchers.
Some parts of the Chapter 3 appeared in:
B. Faraji, W. Shi, D. L. Pulfrey, L. Chrostowski, “Analytical modeling of the transistor laser,” IEEE Journal of Selected Topics in Quantum Electronics,
15(3), 594 - 603, 2009.
B. Faraji, W. Shi, D. L. Pulfrey, L. Chrostowski, “Common-emitter and common-base small-signal operation of the transistor laser,” Applied Physics
Letters, 93(14), 2008.
B. Faraji, D. L. Pulfrey, L. Chrostowski, “Small-signal modeling of the tran- sistor laser including the quantum capture and escape lifetimes,” Applied
Physics Letters, 93(10), 2008.
These articles were co-authored with Wei Shi, Prof. David Pulfrey, and Prof.
Lukas Chrostowski. The author’s contributions in these publications were developing the main idea, numerical simulation, and writing the manuscript.
Wei Shi contributed to the publications through discussions and editing the manuscripts. Prof. Pulfrey and Prof. Chrostowski helped with their numer- ous suggestions in the course of the devolvement of the model. They also assisted by editing the manuscript.
iv Preface
A version of Section 3.4 appeared in:
B. Faraji, N. A. F. Jaeger, L. Chrostowski, “Modelling the effect of the feedback on the small signal modulation of the transistor laser,” Photonics
Society Annual Meeting, Denver, Colorado, US, 2010.
This publication was co-authored with Prof. Nicolas Jaeger and Prof. Lukas
Chrostowski. The author’s contributions in this publication were developing the main idea, mathematical analysis, numerical simulation, and writing the manuscript. Prof. Jaeger and Prof. Chrostowski gave the main idea and assisted in the manuscript writing.
A version of section 3.5 has appeared in:
W. Shi, B. Faraji, M. Greenberg, J. Berggren, Y. Xiang, M. Hammar, M.
Lestrade, Z. Li, S. Li, L. Chrostowski, “Design and modeling of a transistor vertical-cavity surface-emitting laser,” Optical and Quantum Electronics,1
- 8, 2011 (Invited).
This work was co-authored with Wei Shi and Prof. Lukas Chrostowski.
The author’s contributions in this publication were developing analytical and numerical model, simulation, and editing the manuscript. Wei Shi did the numerical simulation with Crosslight and wrote the manuscript. Prof.
Chrostowski initiated the idea to compare the two simulations and param- eter extraction from the numerical simulation and using it in the analytical model.
v Table of Contents
Abstract ...... ii
Preface ...... iv
Table of Contents ...... vi
List of Tables ...... ix
List of Figures ...... x
List of Abbreviations ...... xiii
Acknowledgements ...... xv
Dedication ...... xviii
1 Introduction ...... 1 1.1Motivation...... 1 1.1.1 LaserResonance...... 8 1.1.2 CarrierDynamics...... 9 1.1.3 DeviceandPackagingParasitics...... 9 1.1.4 DriverCircuits...... 10 1.2TransistorLaser...... 10 1.3ThesisObjectiveandChapterSummary ...... 16
2 Direct Modulation of Semiconductor Lasers ...... 19 2.1Introduction ...... 19 2.2RateEquation...... 19 2.3GainCompression...... 28 2.3.1 SpectralHoleBurning...... 29 2.3.2 SpatialHoleBurning ...... 30 2.3.3 CarrierHeating ...... 30 2.4CarrierCaptureandEscape ...... 32
vi Table of Contents
2.4.1 Modeling Using Effective Capture/Escape Lifetimes . 34 2.4.2 Modeling Using Quantum Capture and Escape Life- times...... 40 2.5VCSELParasiticModeling...... 52 2.6ModelVerification...... 53 2.6.1 SamplePreparation...... 53 2.6.2 DCMeasurements...... 55 2.6.3 ACCharacteristics ...... 56
3TransistorLaser...... 62 3.1BipolarJunctionTransistor...... 62 3.2TransistorLaserModeling ...... 65 3.2.1 GeneralConsideration ...... 68 3.3DCAnalysis...... 72 3.4ACAnalysis ...... 78 3.4.1 Common-EmitterConfiguration...... 82 3.4.2 Common-BaseConfiguration...... 85 3.4.3 3rd Order Modulation Response Approximation . . . 95 3.5FeedbackinTL ...... 97 3.6ModelVerification...... 102 3.7Discussion ...... 106 3.7.1 Trade-offbetweenRFGainandBandwidth...... 106 3.7.2 Modeling the Multi-Quantum Well (MQW) TL . . . 109 3.7.3 LimitationoftheDiffusionModel...... 110
4 Large-Signal Analysis ...... 112 4.1Introduction ...... 112 4.2Large-SignalModulation ...... 114 4.3FMAnalysis...... 123 4.4Discussion ...... 124
5 Conclusion and Future Works ...... 126 5.1SummaryandConclusion...... 126 5.2FutureWork...... 129
Bibliography ...... 131
vii Table of Contents
Appendices
A Derivation of the Kirchhoff’s Current Law in the Transistor Laser ...... 138
B Derivation of Charge Conservation for the Virtual States in the QW Region ...... 140
C Publications ...... 141 C.1Peer-ReviewedJournalPublications...... 141 C.2Peer-ReviewedConferencePapers...... 142
viii List of Tables
1.1Opticalcommunicationlinks...... 6
2.1 Simulation laser parameters. The values are chosen for a typical980nmVCSEL...... 23 2.2 Typical simulation laser parameters. The values are chosen fortypical980nmVCSELs...... 49 2.3 Extracted values for the laser modulation transfer function. . 59
3.1 Values of the parameters used in the simulations. The values arechosenfora980nmTVCSEL...... 72 3.2 Equivalent 3rd order model parameter values found by curve- fitting. The two numbers in each row correspond to values for IB = {2IB,th, 3IB,th}...... 97 3.3 Values of the parameters. The first column shows the param- eters, the second column is the value obtained by comparing our model result with the numerical simulation. The third column shows the values we used in our model. The values arechosenfora980nmTVCSEL...... 106
ix List of Figures
1.1SchematicoftheVCSEL...... 3 1.2Fiberopticanaloglink...... 5 1.3Laserdirectmodulationresponselimitation...... 7 1.4SimpleschematicoftheTL...... 11 1.5 Carrier distribution in the SCH region of a conventional laser andbaseregionoftheTL...... 13 1.6SchematicsofthedifferentconfigurationsoftheTL...... 14 1.7TVCSELdiagram...... 17
2.1 Direct modulation response of 1550 nm VCSEL...... 20 2.2 Direct modulation response of the VCSEL using 1-level rate equations...... 24 2.3 Different carrier dynamics involved in the laser operation. . . 29 2.4 Direct modulation response of the VCSEL using 1-level rate equations with gain compression...... 32 2.5CarriertransportinanSCHlaser...... 33 2.6Carriertransportmodel.2-levelsystemforcarriers...... 35 2.7 Direct modulation response of the VCSEL using 2-level rate equations...... 36 2.8Carriertransportmodel.3-levelsystemforcarriers...... 38 2.9Semi-classicalmodelforthecarrierdynamics...... 41 2.10Flowchartofthesimulation...... 48 2.11Carrierdistributionatthedifferentbiascurrents...... 50 2.12 Direct modulation response of the VCSEL using semi-classical model...... 51 2.13Small-signalmodulationbandwidthvariation...... 51 2.14 High speed 850 nm VCSEL in different biasing regimes. . . . 54 2.15DCmeasurementofa850nmVCSEL...... 56 2.16ACmeasurementexperimentalsetup...... 57
x List of Figures
2.17 Measured small-signal modulation responses at different cur- rent injection levels. The low-frequency fluctuations are mainly fromthedetectorusedinmeasurements...... 58 2.18Parasiticestimationmethod...... 60 2.19Parasiticestimationmethod...... 61
3.1Ann-p-ntransistor...... 63 3.2 Carrier diffusion and quantum capture in the QW, and the conduction band energy diagram of the base region...... 66 3.3Minoritycarrierdensitydistribution...... 76 3.4 DC and AC current gain of the transistor and LI curve of the laser...... 77 3.5Common-emitterconfigurationofann-p-nTL...... 83 3.6 Normalized small-signal modulation response of the transistor laser in common-emitter configuration with respect to the differentdevicecurrents...... 84 3.7Common-baseconfigurationofann-p-nTL...... 85 3.8 Small-signal modulation response of the transistor laser in common-emitterandcommon-baseconfigurations...... 86 3.9IntrinsicmodulationresponseoftheTL...... 88 3.10 Current transport factor in common-emitter and common- baseconfigurations...... 89 3.11Small-signalcurrentgainofthetransistor...... 90 3.12 Transfer function for the small-signal modulation of a tran- sistorlaserwithreducedeffectofthetransistor...... 91 3.13 Bandwidth variation of the transistor laser and intrinsic re- sponse,versusDCbiascurrent...... 92 3.14 Energy band diagram of the common-emitter and common- baseconfigurations...... 93 3.15 Curve fitting to the small-signal modulation of the transistor laser in common-emitter and common-base configurations . . 96 3.16Simulationcircuit...... 98 3.17 Small-signal modulation transfer function of the TL with feed- back...... 100 3.18 PICS3D simulation and measurement data. LIV curves of aMQWIn0.17Ga0.83As / GaAs VCSEL. The photolumines- cence data for the simulation and experiments are shown in theinset...... 103
xi List of Figures
3.19 Structure of transistor VCSEL. It is an N-p-n InGaP/GaAs HBT with 30 and 24 pairs of AlGaAs/GaAs layers as bottom andtopDBRs,respectively...... 104 3.19 The LI curve and IC vs IB curve...... 105 3.20 Transfer function of the small-signal modulation of the tran- sistor laser in the common-emitter and common-base config- urations...... 107 3.21 Cascode configuration. Q2 is the TL while Q1 is the driving transistor acting as a high output resistance current source. . 108
4.1Turn-ondelayofaSCHVCSEL...... 114 4.2Turn-ondelay ...... 115 4.3 Turn-on delay for a TL in common-base configuration. Laser threshold is IB,th =1mA.Outputopticalpowerandcarrier density variations are shown. The emitter bias current at + t = 0 increases from zero to IE(0 ) = 46 mA. This value corresponds to the 2IB,th...... 117 4.4 Eye-diagram of the digital modulation of the TL in the common- emitter and common-base configurations for different bit-rates.119 4.5 Eye-diagram of the digital modulation of the TL in the common- emitter and common-base configurations for different bit-rates.121 4.6 Eye-diagram of the digital modulation of the TL in the common- emitter and common-base configurations for different bit-rates.122 4.7 Large-signal FM analysis of the TL in the common-emitter andcommon-baseconfigurations...... 125
xii List of Abbreviations
1D One Dimensional
2D Two Dimensional
3D Three Dimensional
AC Alternative Current
AOC Active Optical Cables
BCB Benzocyclobutene
BJT Bipolar Junction Transistor
DBR Distributed Bragg Reflector
DC Direct Current
DFB Distributed Feedback
DOS Density Of States
DWDM Dense Wavelength-Division Multiplexing
FM Frequency Modulation
FP Fabry-Perot
FTTH Fiber to the Home
GigE Gigabit Ethernet
HBT Heterojunction Bipolar Transistor
LO Longitudinal Optical
NRZ Non-Return Zero
xiii List of Abbreviations
PDF Probability Distribution Function
QW Quantum Well
Rx Receive
SCH Separate Confinement Heterostructure
SL Semiconductor Laser
SMSR Side Mode Suppression Ratio
TL Transistor Laser
Tx Transmit
TVCSEL Transistor Vertical Cavity Surface Emitting Laser
VCSEL Vertical Cavity Surface Emitting Laser
WDM Wavelength-Division Multiplexing
xiv Acknowledgements
I would like to thank a great number of wonderful people who made my experience at UBC memorable.
First and foremost, I would like to thank my supervisor Professor Lukas
Chrostowski for his leadership and support. His passion for scientific prob- lems has taught me a lot. His superb intuition in solving the problems has been a great asset for this project. The open and free environment that
Professor Lukas Chrostowski has created in his laboratory provided me a once-in-a-lifetime opportunity to have a hand in different projects and in- crease my knowledge. He has been a great advisor and a very good friend for me and I will greatly miss him when I leave UBC.
I wish to thank Professor David Pulfrey. We had a very close collabora- tion when I started the modeling of the transistor laser. Professor Pulfrey with his deep knowledge in semiconductor physics and modeling contributed to this project in many situations. I would like to thank Professor Nicolas
Jaeger for his very fruitful discussions on modeling and measurements. Pro- fessor Nicolas Jaeger has generously provided many optical parts needed in the experiments. In the beginning of my PhD, we collaborated with Pro- fessor David Plant’s group at McGill. I would like to thank him for his valuable insights on the various works we did together. I wish to thank Pro-
xv Acknowledgements fessor Markus-Christian Amann and members of his group for providing us with 1550 nm VCSELs that were used in the injection-locking experiments.
I wish to thank my committee members, Professor David Pulfrey, Pro- fessor Konrad Walus, Professor Jeff Young, and Professor David Jones for reading the thesis and giving useful feedback. I wish to thank Professor
Shahriar Mirabbasi for being the chair of the defense session.
I wish to thank my former mentors in Sharif University of Technology:
Professor Sima Noghanian and Professor Foroohar Farzaneh who were my
M.Sc. supervisors. I would like to thank Professor Kasra Barkeshli (RIP) to whom I attribute my passion for electromagnetic theory.
During my PhD, I had the chance to collaborate with brilliant researchers.
I wish to extend my especial thanks to the members of the optoelectronic lab.
They have helped me academically and non-academically. I would thank Wei
Shi, Sahba Talebi Fard, Raha Vafai, Dr. Mark Greenberg, Miguel Guillen,
Xu Wang and former members Eric Kim, Yiyi Zeng, and Qing Gu. I would like to thank Alfred Lam, who helped me to learn the optical measurements upon my arrival at UBC.
The Iranian community in Vancouver is a very friendly society and I have had very good friends with whom I shared many wonderful memories. I wish to thank Maryam Shahrokni, Farid Molazem, Azadeh Goudarzi, Pooya Jafe- rian, Nina Rajabi Nasab, Farzad Moghimi, Nasim Massah, Keivan Ronasi,
Ahamad Ashouri, Nazanin Shabani, and Hamid Mohammadi. I wish that our friendships last forever.
I would like to thank my uncle Vahid who has a very important role in the fact that I chose science as my path in life. I can still taste the sweetness
xvi Acknowledgements of the first science book that he thoughtfully picked for me. That book was my first inspiration, the first magical spark that dragged me towards science and made me step in to the never-ending path of science education for which
I consider my PhD education only a beginning of a lifetime of research and experimentation.
I would like to thank my wife’s family, Fereidoon Edelkhani, Farideh
Kamali, and Nima Edelkhani. I am very proud to be a member of their family and thank them for their generosity, help, and support during the last three years. With their presence in my life I never felt homesick.
I wish to thank my family members. My dad, Sirous, and my mom,
Shahin, are the best parents one can ask for. Their unconditional love and generosity have been the most precious blessings in my life. Words cannot describe how much I love them. My brother, Mehdi, and my sister,
Nastaran, have always been there for me and have kindly helped me to achieve my goals.
The sweetest part of my PhD was when I met Sahar (my wife) and we decided to share the rest of our lives together. She has been my best friend and support. I am blessed to have such a wonderful and beautiful wife. I cannot describe how much I appreciate her sacrifices and encouragements.
Her love, patience, kindness, and sacrifices were the bright light to this journey. She is the shining star of my entire life.
xvii Dedication
This work is dedicated to:
Sahar, my beautiful and wonderful wife,
Sirous and Shahin, my amazing father and mother,
Mehdi and Nastaran, my kind brother and sister.
xviii Chapter 1
Introduction
1.1 Motivation
Lasers came to be during the 1960s. Basically, a laser is an optical oscillator.
Similar to its electrical counterpart, it is a feedback system with an ampli-
fication mechanism. The feedback is provided through the mirrors, e.g., dielectric-air interface in edge emitter lasers and distributed Bragg reflector
(DBR) in vertical cavity surface emitting lasers (VCSEL). Two mirrors along with the material between them compromise an optical resonator [1]. The resonator creates a frequency-selection mechanism. Two conditions must be satisfied to have oscillation:
• The amplifier gain should be higher than the loss in the feedback
system
• The total phase shift in a single round trip must be a multiple of 2π
The first condition is achieved by population inversion via pumping the material and the second condition is satisfied by the optical resonator. The useful output is extracted by coupling a portion of the optical power out of the oscillator.
1 1.1. Motivation
On 16 May 1960 the first laser came out of Hughes Research Laboratories in Malibu, California, USA [2]. The first laser was based on ruby, which was pumped by a pulsed photographic flash-lamp. From that time there has been extensive research and investment put into lasers. Lasers have gone through a myriad of changes and innovations and many new applications have been developed, e.g., optical communication, chip interconnect.
Direct energy gap materials, e.g., GaAs, InP were obvious candidates to generate light. Semiconductor lasers (SLs) began in 1962 with III-V alloys
(GaAs and alloy GaAsP), developed by four research groups [3–6]. In the beginning they were pulse-operated simple pn junctions; they slowly devel- oped into double hetero-structures during the 1970, operating continuously at room temperature. In 1977 quantum wells (QWs) were used in SLs to enhance the density of the states and laser performances [7]. The important properties of the SLs are:
• Small size, e.g., cavity length of distributed feedback (DFB) lasers :
∼ 200 μm and of VCSELs: 1 - 2 μm).
• Low power consumption (VCSELs: few mW, DFB: few 10 mW).
• Direct modulation of the output light.
• Semiconductor based fabrication.
• Wide range of wavelengths and optical powers (from 0.4 to 10 μm).
VCSELs are a class of semiconductor lasers that confine the light through use of the DBRs. Figure 1.1 shows a schematic of a VCSEL. DBRs are fabricated by stacking lattice-matched low and high refractive index layers with the
2 1.1. Motivation proper widths. The gain regions are provided by using QWs. To increase the confinement of the carriers, a separate confinement heterostructure (SCH) is used. For VCSELs based on the AlxGa1−xAs material system one or more oxidation layers are used to confine the pump current to a small area and reduce the threshold current. DBRs are highly reflective, so the cavity is small (1 - 2 μm) and VCSELs essentially are single longitudinal mode lasers and have a low threshold current (< 1mAformesawithraduisof∼ 10 μm)
Direction of the Light
P Contact P-DBR mirror
Oxide Layer QWs and SCH Layer
N-DBR mirror N Contact
Substrate
Figure 1.1: Schematic of the VCSEL. P-doped and n-doped DBRs are used as the mirrors and oxide layer is used to confine the light to small area to reduce the threshold of the laser. Current is pumped from the top contact and QWs are used as the active region. SCH layer is used to confine the electrical carriers.
The material system used in the VCSEL design depends on the applica- tion and consequently on wavelength. For short-range applications (850 nm and 980 nm) DBRs are fabricated by using AlxGa1−xAs material system.
3 1.1. Motivation
Oxide confinement is based on the Al-based layers.
In VCSELs, because of the top-emitting geometry, fabrication costs are reduced. To give a number, a VCSEL in a computer mouse costs just 10 cents to be fabricated [8].
VCSELs have found many applications in the field of optical communi- cation, especially in short-range data transmission. For example, a 12-fiber ribbon cable and a 1x12 array of VCSELs each sending data at 10 Gbps pro- vides 100-Gigabit Ethernet (100 GigE). Such an example of space division multiplexing is just coming onto the market [8].
An emerging application for VCSELs is active optical cables (AOCs).
Datacom companies are making networking easier for data-center companies by attaching optical transceivers to the ends of optical fibers. AOCs use the same pin configuration as the traditional copper cables but carry the signal over an optical fiber. AOCs are much lighter than metal wires. A typical
AOC operates at 850 nm and uses VCSELs at both ends, each working at
5 Gbps or higher.
IBM also used VCSELs in the Terabus project [9]. Terabus was based on a chip-like optoelectronic packaging structure assembled directly onto a card with integrated waveguides. Each Tx or Rx module consists of a 4 x 12 array of VCSELs or photodiodes that are flip-chip bonded to the driver and receiver IC array. Transmitter and receiver operation was demonstrated up to 14 and 20 Gbps per channel.
Figure 1.2 shows a typical optical communication link. It includes a transmitter, transmission medium and a receiver. The goal of an optical link is to send the RF signal so that at the receiver end a replica of the
4 1.1. Motivation
Figure 1.2: Fiber optic analog link. An electrical signal with a center fre- quency of fRF is transmitted by an optical transmitter with a center fre- quency of fOptical. An optical fiber is the communication channel. In the receiver side a high speed photo-detector recovers the electrical signal. signal is reproduced reliably. The details of the optical link (e.g., laser type, modulation scheme, fiber length, and multiplexing method) depend on the application and they vary widely according to the system requirements. Ta- ble 1.1 summarizes the most important properties of optical links. Typically, the fiber, optical amplifiers, photo-detector, and electronic amplifiers have very good performance in terms of linearity. It is the optical transmitter that usually limits the performance of the link. The optical transmitter includes a semiconductor laser at the desired wavelength.
In general there are two ways to modulate laser output power: external modulation and direct modulation. External modulation is achieved by us- ing optical modulators. As it offers the highest performance, it is currently prevalent in most analog links and in digital links with bit-rates above 10
Gbps. Very high bandwidths, > 100 GHz, can be achieved with exter- nal modulators [10]. However, there are several disadvantages: the optical modulator component is bulky, expensive and consumes much RF power.
Furthermore external modulators have an optical loss, typically 3-6 dB,
5 1.1. Motivation 100m Direct channel VCSEL < standards Interconnect 850 nm, 1310 nm protocols and fiber 100 GigE (expected) Dictated by Ethernet 10 GigE, 40 GigE, and 2.5 Gbps, 1.24 Gbps < < WDM Direct Downstream: DFB, Upstream: DFB or FP Upstream: Access (e.g., FTTH) Downstream: Limited to 20national km Telecommunication byUnion Inter- standard Downstream:and/or 1550 1490 nm,1310 nm Upstream: nm, 10 km DFB, Direct Coarse WDM, Metro VCSEL DWDM 10 Gbps > 13101550 nm, nm Table 1.1: Optical communication links. 100 km 10 Gbps > Long-Haul mainly DFB WDM, DWDM or coarse WDM 1550band), nm 15651625 nm (C- (L-band) to Direct or external Speed Distance Laser type Modulation Wavelength Multiplexing Network Type
6 1.1. Motivation
Bias-T
RF DC Laser Diode Laser Diode Laser Diode Package Chip Parasitics Parasitics
H(f) H(f) H(f)
f f f
Figure 1.3: Intrinsic and extrinsic limitation to the laser-chip direct mod- ulation response. Laser is biased by using a DC source and RF signal is added by using a bias-T. The overall direct modulation response of a laser is affected by three sources: Laser intrinsic response (right square), laser chip parasitics (middle square)and package parasitics (left square).
mainly due to coupling loss.
Direct modulation of the laser diode is achieved by modulation of the electrical current which modulates the optical power. This method is easy to implement and has many applications.
In general, the direct modulation bandwidth of a laser is limited by extrinsic and intrinsic effects. The intrinsic effects include laser resonance and carrier dynamics and the extrinsic effects include parasitics (from the chip and packaging) and driver circuits (RF source limitation and bias-T).
Figure 1.3 shows the contribution of the intrinsic and extrinsic limitation to the laser chip direct modulation response. The limitations to laser direct modulation bandwidth are discussed next.
7 1.1. Motivation
1.1.1 Laser Resonance
Experiments have shown the existence of the resonance frequency, referred to as the relaxation oscillation frequency, which results from the interplay between the optical field and the population inversion. The physics of the relaxation oscillation frequency will be discussed in Chapter 2. A low res- onance frequency is the most fundamental limitation on laser bandwidth.
By small-signal analysis of the rate equations, the relaxation oscillation fre- quency can be obtained from [11]: